A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for ExerciseG. B. Whittaker, 1825 - 372 sider |
Fra bogen
Resultater 1-5 af 100
Side 8
... fore- going Rules ( 29 and 30 ) . Examples . 1 2 3 4 5 12 a 2 a 6 ax2 . -7 xyz 17 x y 4 ს +46 5 ax2 5 ax 2 axı 48 ab 8 ab 6 7 axzy 2 ac2x 7 · 5 a2bc . 2 b'x 8 9 3 abc + 8 abz +7 √ax 5 √cy CASE II . When one factor is compound , and ...
... fore- going Rules ( 29 and 30 ) . Examples . 1 2 3 4 5 12 a 2 a 6 ax2 . -7 xyz 17 x y 4 ს +46 5 ax2 5 ax 2 axı 48 ab 8 ab 6 7 axzy 2 ac2x 7 · 5 a2bc . 2 b'x 8 9 3 abc + 8 abz +7 √ax 5 √cy CASE II . When one factor is compound , and ...
Side 82
... fore the last equation in this case will become s ( r — 1 ) = — a , or by a changing the signs of all the terms s ( 1 - r ) = a . ' . s = —— , and TE sa 1-4 S Examples . 1. Find the sum of the series Here a = 3 , r3 and n = 12 , .. 3 ...
... fore the last equation in this case will become s ( r — 1 ) = — a , or by a changing the signs of all the terms s ( 1 - r ) = a . ' . s = —— , and TE sa 1-4 S Examples . 1. Find the sum of the series Here a = 3 , r3 and n = 12 , .. 3 ...
Side 163
... fore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . • Proposition III . Problem . From the greater of two given straight lines to cut off a part equal to the less ...
... fore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . • Proposition III . Problem . From the greater of two given straight lines to cut off a part equal to the less ...
Side 164
... fore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal , ( 4. 1. ) and their ...
... fore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal , ( 4. 1. ) and their ...
Side 170
... fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest that , if two straight lines cut one another , the angles they make at the point where they cut , are together equal to four right angles . COR . 2. And ...
... fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest that , if two straight lines cut one another , the angles they make at the point where they cut , are together equal to four right angles . COR . 2. And ...
Indhold
xi | |
xvi | |
xvi | |
xvi | |
xxvi | |
19 | |
97 | |
108 | |
120 | |
149 | |
159 | |
344 | |
367 | |
387 | |
397 | |
404 | |
410 | |
417 | |
418 | |
426 | |
437 | |
447 | |
576 | |
577 | |
588 | |
607 | |
627 | |
637 | |
651 | |
663 | |
673 | |
687 | |
694 | |
703 | |
709 | |
Almindelige termer og sætninger
ABC is equal altitude angle ABC angle BAC axis bisected centre circle ABCD circumference co-efficient cone conic section convergency curve cylinder described diameter divided draw equal angles equation equiangular equimultiples factors fluxion fore fraction geometrical progression given straight line gnomon greater Hence hyperbola join less Let ABC magnitudes multiple opposite parabola parallel parallelogram perpendicular plane angles polygon prism produced proportional pyramid Q. E. D. PROP Q. E. D. Proposition radius rectangle rectangle contained rectilineal figure remaining angle right angles segment shewn side BC similar sine solid angle solid parallelopiped spherical triangle square of AC subtract surd tang tangent Theorem third tiple triangle ABC vertex whence Wherefore
Populære passager
Side 172 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Side 191 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Side 190 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 196 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 192 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Side 177 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Side 286 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 179 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.